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Existence and exponential decay of solutions to a quasilinear thermoelastic plate system
University of Virginia, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.
London School of Economics, Department of Mathematics.
2008 (English)In: NoDEA. Nonlinear differential equations and applications (Printed ed.), ISSN 1021-9722, E-ISSN 1420-9004, Vol. 15, no 6, 689-715 p.Article in journal (Refereed) Published
Abstract [en]

We consider a quasilinear PDE system which models nonlinear vibrations of a thermoelastic plate defined on a bounded domain in , n ≤ 3. Existence of finite energy solutions describing the dynamics of a nonlinear thermoelastic plate is established. In addition asymptotic long time behavior of weak solutions is discussed. It is shown that finite energy solutions decay exponentially to zero with the rate depending only on the (finite energy) size of initial conditions. The proofs are based on methods of weak compactness along with nonlocal partial differential operator multipliers which supply the sought after “recovery” inequalities. Regularity of solutions is also discussed by exploiting the underlying analyticity of the linearized semigroup along with a related maximal parabolic regularity.

Place, publisher, year, edition, pages
Basel: Birkhäuser , 2008. Vol. 15, no 6, 689-715 p.
Keyword [en]
Quasilinear thermoelastic plates, existence of weak solutions, uniform decays of finite energy solutions
National Category
Mathematical Analysis
Research subject
URN: urn:nbn:se:su:diva-33711DOI: 10.1007/s00030-008-0011-8ISI: 000261985800003OAI: diva2:283407
Available from: 2009-12-25 Created: 2009-12-25 Last updated: 2011-03-14Bibliographically approved

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Maad, Sara
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